# Physics307L:People/Mahony/Eoverm

## e/m Ratio Lab Summary

In this lab Ryan and I tried to find the charge to mass ratio for an electron. We used an apparatus with an electron gun that fired into a helium filled bulb placed inside a magnetic field to excited a ring of Helium atoms. We measured the radius of the ring, and knowing about the Lorentz force, we calculated e/m.

To take data, we let either let the voltage of the electrodes or the current running through the coils be constant, while varying the other parameter. We measured the radius of the rings on the right and the left side using the built in ruler.

## Results

Using the equation

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{e}{m}=\frac{{2}{V}}{{r}^{2}{B}^{2}}\,\!}**

I calculated the following e/m ratios:

- The e/m ratio under constant current and varying voltage was:
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 2.16(2)\cdot 10^{11}\frac{C}{kg}}**

- The e/m ratio under constant current and varying voltage was:
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 2.94(5)\cdot 10^{11}\frac{C}{kg}}**

- The accepted value (from wikipedia) is:
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 1.758820150(44)\cdot 10^{11}\frac{C}{kg}}**

The constant current value was 21 SEMs away from the accepted value, and the constant voltage value was 23 SEMs away from the accepted value.

For our full calcuations and results, see the analysis section of the lab notebook.

## Conclusions

Our values did not overlap with the accepted value primarily because of systematic error. These errors include:

- Electrons not traveling through vacuum
- Electrons possibly not having same energy as helium energy level transitions (Steve Koch 17:47, 15 December 2009 (EST):I don't understand this idea?)
- Electrons traveling in elliptical path
- Parallax